Ecec09presentation

inspectionoptimizationfor MSPS

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

MethodFinding solutions

Part 1: TIC

Part 2: EA

Conclusion

Joint optimization of all inspectionparameters for multi-stage processes:

algorithm, simulation and test set

Sofie Van Volsem

Department of Industrial ManagementGhent University

Bruges, April 15, 2009

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Overview

1 IntroductionMultistage production systemsInspection strategyCost-efficient inspectionProcess model

2 MethodFinding solutionsFirst problem: calculating inspection costsSecond problem: an intelligent solution space search

3 Conclusion

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Sequential linear multistage production system(MSPS)

example: Production of chocolate cookiesproduction stage 1: preparation of doughproduction stage 2: baking of cookiesproduction stage 3: finishing with chocolate

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Sequential linear multistage production system(MSPS)

example: Production of chocolate cookiesproduction stage 1: preparation of doughproduction stage 2: baking of cookiesproduction stage 3: finishing with chocolate

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Inspection strategies for MSPS

An inspection strategy for MSPS isa set of decisions

1 WHERE to inspect:after which of the production stages?

2 HOW STRINGENT to inspect:what are the acceptance limits?

3 HOW MUCH to inspect:all products or only a sample?

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Inspection costs

Costs associated with a selected inspection strategy:1 execute inspection

(test cost, TC)2 repair or replace faulty products internally

(rework cost, RC)3 repair or replace faulty products externally

(penalty cost, PC)

Total costs also includes (loss of) production time,capacity, product image, ...Simplified: more and tighter inspection will lead tohigher quality, but will also induce higher costs.

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Inspection costs

(penalty cost, PC)

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Inspection costs

(penalty cost, PC)

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Inspection costs

(penalty cost, PC)

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Inspection optimization for MSPS: processmodel

For each production stage:Cost parameters(test cost TC, rework cost RC,penalty cost, PC (only after final production stage))Process parameters(process characteristics: mean and variance)Inspection parameters(where, how much and how stringent to inspect?)

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Optimization: what are the decision variables?

Cost and process parameters are given.Only the inspection parameters are decision variables.In multistage systems three types of inspectionparameters can be distinguished, namely

1 inspection type100% inspection (F)sampling inspection (S)no inspection (N)

2 inspection (acceptance) limits3 sampling parameters

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Optimization: what are the decision variables?

Cost and process parameters are given.Only the inspection parameters are decision variables.In multistage systems three types of inspectionparameters can be distinguished, namely

1 inspection type100% inspection (F)sampling inspection (S)no inspection (N)

2 inspection (acceptance) limits3 sampling parameters

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Decision variables: illustration

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Finding solutions

Solution = cost-efficient inspection strategy for MSPSBest solution => lowest total inspection cost (TIC)

1 For every possible solution we need to be able tocalculate TIC

2 Number of possible solutions is infinite=> naive heuristic = calculate every possibility to findthe best = impossible=> development of an intelligent search method =metaheuristic

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Finding solutions

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Finding solutions

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Calculating TIC: formula

TIC = TTC + TRC + TPC (1)with

TTC =n∑

TCi (2)

TRC =n∑

RCi (3)

TPC = cP .dn (4)and with

TCi = cT ,i .(αF ,i .K + αS,i .si) (5)RCi = cR,i .p′i .αF ,i .K (6)

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Calculating TIC: illustration

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Calculating TIC: method

With known defect rates p′i , analytical calculation of TICis straightforward.Alas, no closed analytical formula for p′i available fornon-trivial cases.Definition:

p′i = P [X?i /∈ [LILi ,UILi ]] = 1− P[LILi ≤ X?

i ≤ UILi ]

=> TIC is therefore calculated (approximated) throughMonte Carlo simulation.

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Search strategy: evolutionary algorithm

Applied metaheuristic search method: EvolutionaryAlgorithm (EA)

based on Darwin’s theory on biological evolution:desirable characteristics => better chance of survival=> better chance of transferral to next generation.characteristics "stored" in genes; genes are transferredthrough reproduction/breeding.principles evolutionary algorithm:

1 encoding of candidate solutions;creation of an intital population

2 evaluating and ordering candidate solutions3 creating a new generation of candidate solutions from

promising (parts of) candidate solutions of the previousgeneration

4 iterating steps 2 and 3 until stopping criterium;decoding of "best" solution

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Evolutionary algorithm: example

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Does the method work?

1◦ EA’s convergence is established

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

1◦ EA’s convergence is established

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

2◦ EA’s capability to find meaningful solutions is established

10 processes (A through J) were analyzed and compared

cases A through J process mean exp. valuestep 1 normal µ = 10 10step 2 + normal µ = 10 20step 3 + normal µ = 10 30step 4 + normal µ = 10 40

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

2◦ EA’s capability to find meaningful solutions is established10 processes (A through J) were analyzed and compared

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

2◦ EA’s capability to find meaningful solutions is established10 processes (A through J) were analyzed and compared

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

case A B C D Eall steps σ = 0.1 σ = 0.1 σ = 0.1 σ = 0.2 σ = 0.2penalty 1 000 10 000 100 000 1 000 10 000

case F G H I Jsteps 1&3 σ = 0.2 σ = 0.2 σ = 0.2 σ = 0.1 σ = 0.01steps 2&4 σ = 0.1 σ = 0.1 σ = 0.01 σ = 0.2 σ = 0.2

penalty 1 000 10 000 1 000 1 000 1 000

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Solutions from the case study

case winner solution vector TICA N N N N 45 900B S10.060‖25

9.940‖0 N N F 40.40539.595 67 255

C F 10.0129.988 N N F 40.405

39.595 102 590D S10.210‖100

9.790‖1 N N S40.402‖5039.592‖1 133 450

E F 10.0719.929 N F 31.434

28.566 F 40.40339.5957 178 940

F F 10.1669.834 N N S40.417‖25

39.583‖0 102 935

G S10.034‖259.966‖0 N N F 40.406

39.594 138 015

H S10.165‖1009.835‖1 N F 30.425

29.575 N 72 550

I N N N F 40.41839.582 73 520

J N N N F 40.41139.589 58 840

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Further research

Suggestions:Extensions to the current EA

non-sequential MSPSimperfect inspectionvariable number of simulation runs

further development of standard test setsvalidation through real life case studies

Sofie VanVolsem

IntroductionMSPS

Inspection

Process model

Part 1: TIC

Part 2: EA

Conclusion

Joint optimization of all inspectionparameters for multi-stage processes:

algorithm, simulation and test set

Sofie Van Volsem

Department of Industrial ManagementGhent University

Bruges, April 15, 2009

Ecec09presentation

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